Project Summary The growth and acceptance of wearable devices (e.g., accelerometers) and personal technologies (e.g., smartphones), coupled with larger storage capacities, waterproofing, and more unobtrusive wear locations, has made long-term monitoring of behaviors throughout the 24-hour spectrum more feasible. Wearable devices relevant for human activity (e.g., GENEActiv accelerometer) contain several complementary sensors (accelerometers, gyro, heart- rate monitor etc.) and sample at high rates (e.g., 100Hz for accelerometer). These high-sampling rates and the long duration of capture result in life-log data that truly qualifies as multimodal and big time-series data. The challenges and opportunities involved in fully harvesting these types of data, for widely applicable interventions, suggest that an interdisciplinary approach spanning mathematical sciences, signal processing, and health is needed. Our innovation includes the use of functional-data analysis tools to represent and process the dense time-series data. Functional data analysis is then integrated into machine learning and pattern discovery algorithms for activity classification, prediction of attributes, and discovery of new activity classes. We anticipate that the proposed framework will lead to new insights about human activity and its impact on health outcomes. This interdisciplinary project builds on several research activities of the team. Our past work includes: a) new mathematical developments for computing statistics on time-series data viewed as elements of a function-spaces, b) algorithms for activity recognition that integrate the function-space techniques, and c) data from long-term observational studies of human activity from multimodal sensors. The new work we propose addresses the unique mathematical and computational challenges posed by densely multimodal, long-term, densely-sampled lifelog big-data in a comprehensive framework. The fusion of ideas from human activity modeling, functional-analysis, geometric metrics, and algorithmic machine learning, present unique opportunities for fundamental advancement of the state-of-the-art in objective measurement and quantification of behavioral markers from wearable devices. The proposed approach also brings to fore: a) new mathematical developments of elastic metrics over multi-modal time-series data, b) comparing sequences evolving on different feature manifolds, c) estimation of quasi- periodicities, d) and a new generation of machine-learning and pattern discovery algorithms. The mathematical and algorithmic tools proposed have the potential to significantly advance how wearable data from contemporary devices with high-sampling rates and large storage capabilities are represented, processed, and transformed into accurate inferences about human activity. Wearable devices are becoming more widely adopted in recent years for general health and recreational uses by the broad populace. This research will result in improved algorithms to process the data available from such wearable devices. The long-term goal of the research is to enable personalized home-based physical activity regimens for conditions such as stroke and diabetes.